Got a camera that does 1280 X 720 in AVCHD lite.
I want to edit and burn it to a standard DVD, can this be done and kept in
HD?

I understand that a DVD holds less data than a BR, but this HD video is less than 3GB, well within the space range of a Standard DVD, just not sure if a blu-ray player will play HD material recorded on a standard DVD.

Also what other format can AVCHD Lite be converted to and still maintain
a high def image.

I don't have any web-references to hand but memory tells me that there's no provision in the appropriate specification (can't even remember whether it's the red or the white book) for DVDs to store HD content as anything other than a computer data file. It may be that there are Blu-ray players out their which can recognise such files on a DVD but I think you'd have to delve deeply into the specification of any candidate player to find out.